Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x - 5$ and $ BC = 8x - 9$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x - 5} = {8x - 9}$ Solve for $x$ $ -2x = -4$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({2}) - 5$ $ BC = 8({2}) - 9$ $ AB = 12 - 5$ $ BC = 16 - 9$ $ AB = 7$ $ BC = 7$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {7} + {7}$ $ AC = 14$